Parametric self-excitation in the dynamic cutting system

The problem of ensuring the stability of tool-forming motion trajectories relative to the workpiece, taking into account parametric self-excitation, is considered. The factors causing periodic changes in the parameters of the dynamic cutting system are analyzed. These factors are related to the spatial anisotropy of elasticity properties in the processed workpiece subsystem, variations in the allowance around the perimeter of the workpiece rotation, kinematic disturbances from the mechanical parts of the machine tool’s drive units, and periodic processes in the cutting zone. A generalized dynamic model of the system with periodically varying parameters is presented. The influence of periodically changing parameters on the stability of the trajectories is studied. The specific features of stability loss in dynamic cutting systems are revealed. In particular, it is shown that due to parametric effects, as cutting speed increases and spindle rotation frequency rises, there is always a critical frequency at which the system loses stability.